2 Solutions for integral 1/(2x) dx ???

[dagr8est]

integral 1/(2x) dx

u=2x
du=2dx

= 1/2 integral(1/u) du
= 1/2 ln|u|+C
= 1/2 ln|2x|+C

or

integral 1/(2x) dx
= 1/2 integral 1/x dx
= 1/2 ln|x|+C

Why am I getting 2 different answers? Is it because of the +C?

 

[pka]

"Why am I getting 2 different answers? Is it because of the +C?"
Yes indeed.
Note that ln(|2x|)=ln(|x|)+ln(2) and ln(2) is a constant.